Does there exist a (1/3)-Koide formula that allows some quarks to have charge ± 1/3 ?
From Wolfram Alpha:
(muon mass) /(electron mass) = 206.7683
(tauon mass)/(electron mass) = 3477.48
(59^3 + 33 * 59^2 + 57 * 59 + 9 )^(1/27) - 1.59983643131952544 = 0 approx.
For a = 1.5998364, x = 206.7683, y = 3477.48,
calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333333
For the polynomial x --> x^3 + 33 * x^2 + 57 * x + 9 my guess is that 33 + 26 = 59 is meaningful because of 26-dimensional bosonic string theory and the fact that the three primes 59, 59 ± 12 divide the order of the monster group. My guess is that the constant term 9 is meaningful because of Lestone's heuristic string theory.
Note that 8/5 - 1/(32 * 191) = 1.599836874 ...
For a = 1.5998369, x = 206.7683, y = 3477.48,
calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333332
Note that 191 = 2 * 72 + 47 and 47, 59, 71 are the 3 largest primes that divide the order of the monster group.
Monster group, Wikipedia